Play style
The play style to take advantage of the Ambassador is something like a behind-enemy-lines sniper. The best way to think about is is as a long-range back stab, since it requires precision to use effectively, but when you are successful, you will take down enemies very quickly.
Ambassador = alternatives
Per usual, your goal as a Spy is to sneak behind your enemies. Normally, your next goal, apart from sapping the Engineer's structures, would be to get in position to back stab your enemies, but with the Ambassador, you have the option of trying to get in a few quick head shots instead, which lets you attack your enemies from further behind than normal, allowing you to play more cautiously than normal as well.
Ambassador vs Revolver
Since the Ambassador emphasizes head shots, and since head shots are easier to get on enemies who are unaware of your presence, the Ambassador is more suited for initiating conflict in situations where a back stab attempt is unfeasible or risky, such as when you come across a sniper equipped with the Razorback, or a Pyro. It would be better thought of as a weapon suited for 'back-of-the-head' shots rather than one simply suited for head shots.
The basic Revolver is more suited to ending conflict by finishing off survivors of failed back stab attempts, or holding off enemies who are pursuing you. Also, since it is normally more powerful than the Ambassador, it is also better for finishing off the Engineer's structures, especially after you have begin sapping them.
Summary
If you are successful at sneaking behind enemy lines but have difficulty in getting up close for back stabs, the Ambassador can be an effective alternative.
Most items have a set number -- before the Scout update introduced the Sandman, no item went higher than level 10.
About the time of the Spy / Sniper update, there was a glitch in the random drop system, and normal weapons (that usually have a fixed level number) were generated with a random level between one and one hundred. This has since been fixed, so if you see, to use one of my own items for example, a level 56 Dead Ringer, that means the item is very old. (And now with the latest patch, you'll never see a non-vintage oddly leveled item)
On the other hand, hats will always have a random level. This means nothing, but certain levels are certainly more valuable for trading, for pure sentimental value. (1, 100, 69, 42, etc.)
The singular exception to all of the above is the new Dueling Badge medal misc item, which actually "levels up" as you kill folks during your duels. A level 100 dueling badge works out to 1000 kills (Might be off a factor of ten) during duels, and likewise the rarity of the badge itself (bronze, silver, gold, platinum) is based on level increment. 0-25,26-50,51-75,76-99,100, etc.
In no case does the level of an item have any effect on gameplay.
Best Answer
You're not wasting the speed of the scout in arena. Running into a group of 12 people is pretty much guaranteed death.
Scout in arena is exactly as you're doing. You need to wait for people to spread out and rely on your teammates audio cues and voice communications to know where to go. Listen for sniper calls or watch the death tracker for sniper kills and then go pick them off. Pick off stragglers who might be retreating to find health after a larger fight. Arena means that every death is a tip in balance, and as you're the MOST fragile player, you've got a lot of liability on your shoulders to ensure that you don't waste your life right off the bat (no pun intended). Use your double jump to your advantage and consider using the FaN to get to good ambush / hiding spots.
Scout in arena can also be effective bait. Get that demo to chase you around the corner into the hands of a heavy/medic combo. A lot of people will tunnel vision and auto target scouts due to their low health.
To put it simply, if you're playing scout in arena, you're playing more like a spy in any other match.
Edit: Adding in a bit about defensive play.
You can also treat scout in arena like a 6v6 competitive match as the defensive scout. Your job is to protect the medic who will likely be glued to a soldier or heavy early on. If the offensive target (heavy or soldier) is an attentive player, the FaN is a great choice for this due to it's stopping power, buying them a few seconds to turn and destroy (assuming they're not dead already). If they're not terribly attentive, your normal scattergun will do the trick and you're just going to be trying to kill and dodge.
Lastly, while I don't use it often (I love me some pistol action), you can use the Bonk! Energy Drink and park yourself between the medic and his assailant to effectively create a wall for 6 seconds while the heavy / soldier / whatever has time to refocus and destroy them.
Moral of the story: Medics can win arenas. Treat them well.